Everything You Need to Know About Sketching Curves Using Derivatives
TL;DR: Curve sketching is a checklist sport. You note the domain, find intercepts and asymptotes, use the first derivative to track slope and critical points, and use the second derivative to nail down concavity and inflection points. Hit every check, plot the key landmarks, and the graph practically draws itself. Skip a step and the […]
Differentiability: Everything You Need To Know
Differentiability and Smoothness: A function is differentiable at a point if it is “smooth” (without sharp corners or cusps) and continuous at that point. The smoothness implies that the function’s graph can be approximated by a tangent line at every point where the function is differentiable. Differentiability and Continuity: While differentiability implies continuity, the converse […]
